You sure can Ilaria!
Simply proceed with the standard installation / activation process that you went through the first time. Should you run into any activation issues, please contact out Licensing Assistance team for the necessary assistance.
I also wanted to point out that for future reference you can utilize the LTU prior to re-formatting, which would allow you to export and import the existing license.
Please accept as a solution, or reply with additional questions if needed.
I thought there were restrictions for the EDU-license.
Very useful the link you gave me. Saved in the bookmarks!